Substitution and elimination are two symbolic techniques used to solve linear equations. For example, if it is easy to set up an equation for substitution where 1 variable is on 1 side, then use that; For example, 4y=16+4x, you can easily divide by 4, get y=4+x (or y=x+4), and plug that into the other equation. In other cases where it may not be so easyFractions/decimals, etc., then you would probably rather use elimination.

1) The substitution method. This method is best utilized when one of the variables in one of the equations has a coefficient of 1 or -1, otherwise you will introduce fractions. Substitution can also be used for nonlinear systems of equations.
(2) Linear combinations also called the elimination method, multiplication and addition method, etc... My personal favorite as it can be done efficiently. It generalizes well to larger systems and is the underpinning of various other solution methods.
As the name implies it requires the equations to be linear.
You need to know both and be comfortable switching between them.

Can we get one for the elimination method too?
Also, can you solve the same problem using either of the two techniques?

Answers

Answer 1

Answer: A simple sample problem for Elimination:

x - y = 1
x + y = 5

You can solve the same problem using either technique, as far the equations are linear equations.

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Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm. a. What is the volume of the cylinder? Explain your method for finding the volume. b. What is the total volume of the three balls? Explain your method for finding the total volume. c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.
Write a compound inequality that represents the situation. all real numbers at least –6 and at most 3A. –6 ≥ x ≥ 3 B. –6 < x ≤ 3 C. –6 ≤ x ≤ 3 D. –6 < x < 3
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The distribution of the weights of a sample of 1,500 cargo containers is symmetric and bellshaped. According to the Empirical Rule, what percent of the weights will lie: a. According to the Empirical Rule, what percent of the weights will lie between formula73.mml b. According to the Empirical Rule, what percent of the weights will lie betweenformula75.mml and student submitted image, transcription available below+1s c. Below formula75.mml-1s

Answers

Answer:

Step-by-step explanation:

According to the Empirical Rule, for a symmetric and bell-shaped distribution:

a. Approximately 68% of the weights will lie between formula73.mml. This means that about 34% of the weights will lie to the left of formula73.mml, and about 34% of the weights will lie to the right of formula73.mml.

b. Approximately 95% of the weights will lie between formula75.mml and formula75.mml +1s. This means that about 47.5% of the weights will lie to the left of formula75.mml +1s, and about 47.5% of the weights will lie to the right of formula75.mml.

c. Approximately 68% of the weights will lie below formula75.mml-1s. This means that about 34% of the weights will lie to the left of formula75.mml-1s.

These percentages are approximate values based on the Empirical Rule and provide a general understanding of the distribution of the weights in a symmetric and bell-shaped distribution.

Use your completed 24-hour circle to calculate how much time you spend on each activity listed in the Activities Breakdown below each week. The blank lines are for any additional situations that take up your time. After you have totaled up all the items you can think of, figure out how much free time you have. ACTIVITIES BREAKDOWN - Hours per week 2. Study Time, reviewing, projects, papers 3 11. ____ 12.___ 13. Wasted hours ___ A. Sleep B. Work C. Leisure D. Wasted hours

Answers

Answer:

To calculate how much time you spend on each activity, you need to fill in the circle with everything you do in a day, using 24-hour format1. For example, if you sleep for 8 hours, work for 4 hours, and study for 3 hours, you can write these numbers in the circle. Then, you can add up the hours for each activity and write them in the table below.

Here is an example of how to fill in the circle and the table:

|-----------------|

| |

| 8 4 |

| / \ / \ |

| / \/ \ |

| / /\ \ |

|/ / \ \ |

| / \ \ |

| / \ \|

| / \ /|

|/ \ / |

| X |

| / \ |

| / \|

| / |

| 3 |

| |

|-----------------|

ACTIVITIES BREAKDOWN - Hours per week

1. Class Time: 0

2. Study Time, reviewing, projects, papers: 3 x 7 = 21

3. Commuting: 0

4. Dressing and eating: 1 x 7 = 7

5. Hours of employment: 4 x 5 = 20

6. Responsibilities at home: 1 x 7 = 7

7. Athletics requirements: 0

8. Telephone and computer: 2 x 7 = 14

9. Television: 1 x 7 = 7

10. Sleeping: 8 x 7 = 56

11.

12.

13. Wasted hours:

Total: (21 + 7 + 20 + 7 + 14 + 7 +56) =132

Total number of hours per week =168

Subtract your Total (132)

Total free hours per week = (168 -132) =36

Step-by-step explanation:

Simplify 3x times 1/x to the -4 power times x to the -3 power

Answers

Answer:

3x²

Step-by-step explanation:

$3x\cdot(1)/(x^(-4))\cdot x^(-3)=3x^((1-(-4)-3))=3x^2$

___

The applicable rules of exponents are ...

$x^ax^b=x^(a+b)\n\n(1)/(x^(-a))=x^a$

Answer:

3x^2.

Step-by-step explanation:

3x * (1/x)^-4 * x^-3

= 3x * x^4 * x^-3

= 3x * x

= 3x^2.

If x is a real number such that x³ = 64, then x² + √x =?

Answers

$x^3 = 64\n \nx=\sqrt[3]{64}\n \nx=4 \n \n \n x^2 + √( x )=4^2+√(4)=16+2 =18$

If x³=64
,x=∛64=4
x²=16
√x=4
x²+√x=16+2
⇒18

in sunlight, a vertical stick 9 ft tall casts a shadow 7 ft long. at the same time a nearby tree casts a shadow 28ft long. how tall is the tree? round to the nearest tenth

Answers

the tree wood b 36 ft
because:
28'
7' = 4'
9'x4'= 36'
that 36' is the trees height.

Answer:

36.0ft

Step-by-step explanation:

What is the degree of each monomial?
-9

a. -8
b. 0
c. -10
d. -9

Answers

Any monomial without a written exponent has a degree of 1.

$-9^1=-9$

it is (D) = -9 $9^(-1) = -9$

Other Questions

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The Murphys’ gross annual family income is $120,500. Mr. Murphy referred to the graph shown below and calculated that his family will spend $28,920 on taxes this year. What is wrong with Mr. Murphy’s calculation?a.He has calculated only federal taxes.b.He has calculated only state taxes.c.He does not need to include federal taxes.d.He does not need to include state taxes.

If a man can run p miles in x minutes, how long will it take him to run q miles at the samerate?

Need help with this. Show your steps so I could check my work and my answer.